Improved Quantum Metrology Using Quantum Error Correction

We consider quantum metrology in noisy environments, where the effect of noise and decoherence limits the achievable gain in precision by quantum entanglement. We show that by using tools from quantum error correction this limitation can be overcome. This is demonstrated in two scenarios, including a many-body Hamiltonian with single-qubit dephasing or depolarizing noise and a single-body Hamiltonian with transversal noise. In both cases, we show that Heisenberg scaling, and hence a quadratic improvement over the classical case, can be retained. Moreover, for the case of frequency estimation we find that the inclusion of error correction allows, in certain instances, for a finite optimal interrogation time even in the asymptotic limit.

Figure 1

Illustration of a quantum metrology scenario using error correction. We consider $N$ blocks of size $m$ (here $m=5$). In scenario I, all particles in each block are affected by a Hamiltonian $H_{\mathrm{I}}=1/2{\sigma }_z^{\otimes m}$. In scenario II, only the lowest (green) particle of each block is affected by the Hamiltonian $H_{\mathrm{II}}=1/2{\sigma }_z^1$, and $m-1$ ancilla particles (red) are used to generate an effective $m$-body Hamiltonian. In both scenarios, all particles are affected by (local) noise, and each block serves to encode one logical qubit.